It has a bearing, but the engine's not going to override your settings (at least it's not supposed to). If your PH setting is 0 or 1, you'll almost never see a PH'er, regardless of the score; if your pitcher has a pull setting of 1, and he's not near his PC, he probably won't be removed.
If you want your pitchers to be PH for in situations like you described above, I'd recommend you keep your PH/pull settings at a minimum of 3, and of course make sure you've got PH checked next to your pitcher's name in Advanced Settings.